1 Objective 1

Our overarching objective is to determine the impact of pulse consumption on key risk factors for metabolic and inflammation-based diseases in overweight and obese humans. Using a 12-week controlled, randomized clinical trial of lentil, chickpea or black bean consumption in this population, we will achieve the following specific objectives: (1) Determine the impact of lentil, chickpea, or black bean consumption on postprandial triglyceride and inflammation responses to a high-fat meal challenge and basal (fasting, resting) markers of metabolic health (glucose, lipids, insulin, inflammation, visceral adiposity). […]

1.1 Summary

  • 5% significance: If all participants recruited have high postprandial triglyceride response (TGR, peak TGR is greater than 60 mg/dL), a total sample size of n = 36 (18 per group) to 48 (24 per group) can detect a 50% decrease in the peak TGR score at 5% significance with 76% to 86% power, respectively. If both high and low TGR people are recruited with the same 22:18 ratio as in the preliminary study, a total sample size of n = 36 (18 per group) to 48 (24 per group) can detect a 50% decrease in the peak TGR score at 5% significance with 43% to 53% power, respectively.

  • 10% significance: If all participants recruited have high postprandial triglyceride response (TGR, peak TGR is greater than 60 mg/dL), a total sample size of n = 36 (18 per group) to 48 (24 per group) can detect a 50% decrease in the peak TGR score at 10% significance with 86% to 93% power, respectively. If both high and low TGR people are recruited with the same 22:18 ratio as in the preliminary study, a total sample size of n = 36 (18 per group) to 48 (24 per group) can detect a 50% decrease in the peak TGR score at 10% significance with 58% to 67% power, respectively.

  • If other inflammation responses are tested, a multiple testing correction has to be applied to keep the family-wise significance at a specified level to avoid the Type I error inflation.

The remainder of this report details our methodology for power analysis.

1.2 Overview

The participants of the study have to meet some inclusion criteria. They will then be randomly assigned to either treatment (having lentil, chickpea, or black bean) or control group (usual meal). At the beginning of a 12-week-long study, the triglyceride (TG) and inflammation responses will be measured before (the baseline) and then several times after consuming a high-fat meal. The changes in TG from the baseline (TGR) will be calculated and the peak change (TGR_max_0) will be recorded. Whoever has their TGR_max > 60 mg/dL will be put into HI responders group and others will be put into LO responders group. During the 12-week trial, the participants will be offered midday meals every weekday based on their treatment/control group. At the end of the study, the same test will be done again and the participant’s peak TGR_max_1 will be then compared to their TGR_max_0 to see if there is a meaningful decrease in the treatment group that makes them different from the control group.

1.3 Preliminary data

A similar study was done in the past but at a one-time point. Some of the summary information is displayed below. This data set will be used to calculate the effect size for the power analysis.

sample min Q1 median Q3 max mean sd n missing
High and Low Responders -9 40 66 112 366 88 82 40 0
High Responders Only 62 78 110 158 366 134 84 22 0

1.4 Power Analysis

1.4.1 Effect Size

Using the preliminary data, the effect size is estimated as

\[Cohen's\ d = \frac{\mu_{trt} - \mu_{ctrl}}{sd}\] where \(\mu_{trt}\) is the true change in peak TG value in the treatment group, \(\mu_{ctrl}\) is the true change in peak TG value in the control group, and \(sd\) is the standard deviation of each group (assuming that two groups have equal variance). The researcher cited a previous study on mice that observed the peak TG value decreases 50% on average in the treatment group. Also, it is expected that the change in peak TG value in the control group is minimal so we set \(\mu_{ctrl} = 0\). The effect size in terms of Cohen’s d for each target sample is calculated in the following table

sample mean before expected mean after standard deviation effect size
High and Low Responders 88 44 82 0.54
High Responders Only 134 67 84 0.80

1.4.2 Analysis Plan

Two-sample t-test for the difference in the peak TGR change between the two groups will be performed. Because we expect the values of TG decrease after the 12-week challenge, we use the one-sided version of t-test.

Besides TG, the researcher may look at the difference in change of pro-inflammatory responses, including 4 types of cytokines, TNF-alpha, and GM-CSF between two groups. If it happens, some multiple testing correction needs to be applied to account for the Type I inflation problem in multiple testing. For the sake of simplicity in this power analysis, we use Bonferroni correction with the family-wise significance level of either 0.05 or 0.1.

1.5 Power Analysis Using TG High Responders Only

1.5.1 Power vs. Sample Size with family-wise p-value = 0.05

1.5.2 Power vs. Sample Size with family-wise p-value = 0.1

1.6 Power Analysis Using Both High and Low TG Responders

1.6.1 Power vs. Sample Size with family-wise p-value = 0.05

1.6.2 Power vs. Sample Size with family-wise p-value = 0.1